I am a 2nd year master's students in Pure Mathematics.

I am interested in knowing how should I compare the research of 2 pure mathematicians working in same field, say topology. I want to work with one of them for my master's thesis. Both have the same specialization. This will also help me to know which is better for PhD applications. One way I do this is, I go to their Google Scholar profile of Prof A and Prof B and see who has been cited more. The more someone is cited the better.

But, I am not able to think of any other parameters. One can think of who has published more papers and divide each paper by number of co-authors and then do a total.

I am asking this assuming both work in same branch of pure mathematics.

  • 43
    For your purposes, helpfulness is more important than reputation. Some top scholars are too busy to help you effectively, likewise untenured faculty. Ask other students, more advanced than yourself, what to expect from each.
    – Buffy
    Jul 5, 2022 at 16:29
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    I'll leave it to others to tell you why this is a bad idea in general and just note that unnormalized quantities like the total number of papers will only tell you which one is older...
    – mlk
    Jul 5, 2022 at 16:43
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    Flipping a coin probably works as well as anything else.
    – Jon Custer
    Jul 5, 2022 at 21:27
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    As a masters student, you presumably have an adviser, who could give you better information than counting papers, citations, etc. (I didn't say "perfect information", just "better information".) And you could ask a few other faculty members for advice too. Jul 6, 2022 at 1:39
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    "The more someone is cited the more the better." This is the very wrong assumption you are having. Being a good researcher (may) imply having a lot of citations, but the opposite is absolutely not true. Additionally, you may expect some difference if one has 10'000 citations and the other has 100, but any difference smaller than 2 order of magnitudes tells you nothing about quality. And let's not start the discussion about the h-index or related metrics, which clearly tells you at which stage of their academic career is someone, and nothing more.
    – EarlGrey
    Jul 6, 2022 at 12:12

4 Answers 4


Go and talk to them (each one separately), and have a conversation about your interests, their interests, and what kind of Master’s thesis projects each of them might be able to supervise you to work on.

Also, if you are able to talk to their former and current students, get their take on what each of the two professors is like to work with. That sort of feedback could be very valuable.

Remember, you are trying to find the best thesis adviser, not the best researcher. Those two qualities are far from identical and do not necessarily align. Thus, the professors’ publication records will not necessarily help you and may even mislead you to make a drastically wrong choice.

At the end of the day, it’s probably best to go with your gut about which prospective adviser’s attitude and skills are the best fit for you, after doing the research I’m suggesting above. The relationship between a student and adviser depends closely on psychological factors which cannot be captured by how the two professors look “on paper”.

Finally, it’s good to keep in mind that the professors too may be evaluating your fit to be their student. Don’t assume that you necessarily get to choose, or act entitled like you’re interviewing them for a job and they need to impress you with how cool they are. (It may in fact be more helpful to adopt the mindset that it’s you who needs to impress them. But mainly you should approach the conversation as a professional interaction in which two people are considering helping each other reaching a shared goal. In other words, act neither entitled nor obsequious.)

Good luck!

  • 5
    you are trying to find the best thesis adviser, not the best researcher Voted up for this. Talking to their students (discretely) is really good advice. Jul 7, 2022 at 15:21
  • Just to tack on something about following the former students: even if you aren't able to speak to many/any of them you can usually see where they went on to work. If at least one of them got the kind of position you want, that's a good sign. Ultimately, though, you need to understand the personalities and that there will always be risks and unknowns. Jul 8, 2022 at 15:30

It's complicated. This exact same problem is encountered when universities have to hire a new professor, choosing among several candidates. The only satisfying solution people have found is having a committee with several experts in the field (say geometry/topology) review their work, interview them, and spend a nontrivial amount of time in the process. Often there are disagreements. If universities could replace all this work with a simple Google Scholar search, they would do that in a heartbeat. :)

Bibliometric indices can help you tell a poor mathematician from a great one, but when ranking people of similar level there are so many confounding factors that they become unreliable. In addition, as the comments note, "which one has the better research output" is a very different question from "which would be a better advisor".

So unfortunately there is no short answer: read about them and their research, check their website, ask around to other students and faculty, and try to form an opinion based on this. But unless you find major visible differences, the answer is probably going to be that they're both good choices for your future.

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    I wouldn’t say it’s the “exact same problem”. In hiring, the main thing departments are trying to evaluate is how strong of a researcher someone is. This is quite a different parameter from how good someone will turn out to be as a graduate adviser, and it seems to me that evaluating these two distinct parameters call for quite different methodologies.
    – Dan Romik
    Jul 6, 2022 at 5:05

The kind of reductionist task you are attempting is quite dangerous. Researchers are also persons and you want to consider (if only in the abstract) the pros and cons of working with a well-cited researcher who happens to have issues when dealing with others and/or graduate students.

In research and in graduate studies, personalities matter because research is done by humans and not by drones (at least not yet).

I suggest you consider talking with current and former students to find out the atmosphere in the group. Does this or that person send graduate students to conferences, and how often? Do they send graduate students on academic visits or summer schools? Do they encourage students to meet with guests, or guests speakers? Do they “promote” the work of their students of keep the spotlight for themselves? Do they have transparent guidelines and expectations for the funding of students and their activities? None of these would show up on a Google profile or in a citation index.


It almost sounds like you are trying to optimize a career path, rather than start a research career. If so, I think that's quite misguided, from almost any angle. If you aren't fundamentally guided by a passion for something in math, and make your choices on that basis, I doubt counting citations is going to help you.

In my experience, I've seen very few mathematicians focus on career path and come away happy and successful. Math research isn't a corporate hierarchy. Many of the most successful researchers I've known, just worked very hard, often for years in relative obscurity, pursuing an original program. The payoff came when they had interesting results, not when they had enough social connections and bullshit to fill their resume.

How do you imagine the number of times a professor has been cited, to affect your work? Are you hoping that you'll hitch to the bandwagon of a hot, emerging field?

I've known a few highly talented students who ended up with illustrious, Fields Medalist, advisors, where it probably backfired from a career view. The problem is that being a Fields Medalist doesn't mean being generous with students, writing compelling, or even fair, recommendations, having realistic expectations, encouraging or advising well, or being an engaged advocate. I'm sure most people who've sat on a hiring committee have read stellar recommendations for mediocre students with generous advisors, and mediocre recommendations for stellar students with arrogant advisors.

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